
EXAMPLE

Given triangle A173305, we create an array by extracting terms in powers of A173305:
1, 1, 1, 2, 2, 3, .4, .5, .6, .8, 10, 12, 15,...; = column terms of A173305
1, 1, 2, 3, 4, 6, .9, 12, 16, 22, 29, 38, 50,...; = terms of A173305^2
1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 72,...; = terms of A173305^3
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77,...; = terms of A173305^4
...
(rows quickly converge to A000041, the partition numbers).
Taking finite difference terms from the top, we obtain the array:
1, 1, 1, 2, 2, 3, .4, .5, .6,..8, 10, 12, 15,...;
......1, 1, 2, 3, .5, .7, 10, 14, 19, 26, 35,...;
............1, 1, .2, .3, .5, .7, 11, 15, 22,...;
...........................1, .1, .2, .3, .5,...;
...
Finally, columns of the above array become rows of A173306:
1;
1;
1, 1;
2, 1;
2, 2, 1;
3, 3, 1;
4, 5, 2;
5, 7, 3;
6, 10, 5, 1;
8, 14, 7, 1;
10, 19, 11, 2;
12, 26, 15, 3;
15, 35, 22, 5;
18, 46, 30, 7;
22, 60, 42, 11;
27, 78, 56, 15;
32, 100, 76, 22, 1;
38, 128, 100, 30, 1;
46, 162, 133, 42, 2;
54, 204, 173, 56, 3;
...
